Quantum Graph Neural Networks (QGNN) are a new class of quantum neural network ansatz which are tailored to represent quantum processes which have a graph structure. They have application in simulating Hamiltonian dynamics of quantum systems. The topology of the graph plays an important role, e.g. in inferring stability of steady states. They also manage to reproduce transmission fluctuations and can be generalized to the nonlinear domain. In this work, we adapt QGNN for simulating electronic dynamics in condensed matter systems. We are particulary interested in Fermi-Hubbard model in line with this, we investigated time evolution and scaling of Majonara Hubbard Model. We employ Quantum Autoencoder architecture to be able to simulate fermionic wavefunction in latent space using compressed wavefunctions propagation in time.
Quantum Graph Neural Networks (QGNN) are a new class of quantum neural network ansatz which are tailored to represent quantum processes which have a graph structure. They have application in simulating Hamiltonian dynamics of quantum systems. The topology of the graph plays an important role, e.g. in inferring stability of steady states. They also manage to reproduce transmission fluctuations and can be generalized to the nonlinear domain. In this work, we adapt QGNN for simulating electronic dynamics in condensed matter systems. We are particulary interested in Fermi-Hubbard model in line with this, we investigated time evolution and scaling of Majonara Hubbard Model. We employ Quantum Autoencoder architecture to be able to simulate fermionic wavefunction in latent space using compressed wavefunctions propagation in time.
We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed quantum systems over a quantum network. Along with this general class of ansatze, we introduce further specialized architectures, namely, Quantum Graph Recurrent Neural Networks (QGRNN) and Quantum Graph Convolutional Neural Networks (QGCNN). We provide four example applications of QGNNs: learning Hamiltonian dynamics of quantum systems, learning how to create multipartite entanglement in a quantum network, unsupervised learning for spectral clustering, and supervised learning for graph isomorphism classification.
We develop and implement two realizations of quantum graph neural networks (QGNN), applied to the task of particle interaction simulation. The first QGNN is a speculative quantum-classical hybrid learning model that relies on the ability to directly utilize superposition states as classical information to propagate information between particles. The second is an implementable quantum-classical hybrid learning model that propagates particle information directly through the parameters of RX rotation gates. A classical graph neural network (CGNN) is also trained in the same task. Both the Speculative QGNN and CGNN act as controls against the Implementable QGNN. Comparison between classical and quantum models is based on the loss value and accuracy of each model. Overall, each model had a high learning efficiency, in which the loss value rapidly approached zero during training; however, each model was moderately inaccurate. Comparing performances, our results show that the Implementable QGNN has a potential advantage over the CGNN. Additionally, we show that a slight alteration in hyperparameters in the CGNN notably improves accuracy, suggesting that further fine tuning could mitigate the issue of moderate inaccuracy in each model.
Abstract Graph neural networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum computing offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, quantum GNNs (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the guided graph compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. We compare GGC to a model that uses the autoencoder as a preprocessing step and to a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.
We present a graph-based machine-learning framework for simulating the time evolution of electronic wavefunctions and densities in quantum systems. Inspired by parallels between time-dependent quantum propagators and spectral graph convolutions, we employ a recursive Chebyshev graph neural network architecture capable of learning the dynamics of electronic processes across a range of external potentials and Hamiltonians. Two model variants are introduced: one that evolves the full complex-valued wavefunction and the other that propagates only the electron density. Both models are trained on trajectory data generated from tight-binding Hamiltonians and a time-dependent electron-phonon coupled system. Our results demonstrate that wavefunction-based models achieve near-exact long-time propagation across static and dynamic regimes, while density-only models maintain strong performance using physics-informed loss functions, even in the absence of phase information. This work lays the foundation for coarse-grained, resolution-independent propagators for electronic dynamics and opens new pathways for scalable quantum simulations in complex molecular and condensed-phase systems.
Graph Neural Networks (GNNs) are now one of the key tools to model relational and non-Euclidean data in multiagent systems, infrastructure networks and even molecular modeling applications. Nevertheless, in very dense or noisy graph topologies, classical message-passing architectures may experience scalability and representational degeneration, especially due to over-smoothing and insufficient higher-order dependency information. The recent developments in quantum machine learning indicate that hybrid quantum-classical models can also provide an alternative feature representation by projecting relational data to parameterized quantum circuits. This article presents a Quantum-Enhanced Graph Neural Network (QGNN) architecture that extends variational quantum circuits with graph learning pipelines, based on classical learning. Parameters are represented as parameterized qubits, and relational dependencies are represented as structured entanglement mappings. We benchmark the regimes where quantum-enhanced relational encoding proves to be more robust and stable through the swarm coordination, molecular property prediction, and financial transaction network. We also elaborate on the issue of scalability, hardware issues, and practical aspects of near-term hybrid implementations and give a critical view of the changing role of quantum methods in computational intelligence systems.
Graph Neural Networks (GNNs) are now one of the key tools to model relational and non-Euclidean data in multiagent systems, infrastructure networks and even molecular modeling applications. Nevertheless, in very dense or noisy graph topologies, classical message-passing architectures may experience scalability and representational degeneration, especially due to over-smoothing and insufficient higher-order dependency information. The recent developments in quantum machine learning indicate that hybrid quantum-classical models can also provide an alternative feature representation by projecting relational data to parameterized quantum circuits. This article presents a Quantum-Enhanced Graph Neural Network (QGNN) architecture that extends variational quantum circuits with graph learning pipelines, based on classical learning. Parameters are represented as parameterized qubits, and relational dependencies are represented as structured entanglement mappings. We benchmark the regimes where quantum-enhanced relational encoding proves to be more robust and stable through the swarm coordination, molecular property prediction, and financial transaction network. We also elaborate on the issue of scalability, hardware issues, and practical aspects of near-term hybrid implementations and give a critical view of the changing role of quantum methods in computational intelligence systems.